Theories of thermal stresses based on space–time-fractional telegraph equations

The generalized telegraph equations with time- and space-fractional derivatives are considered. The corresponding theories of thermal stresses are formulated. The proposed theories interpolate the classical thermoelasticity, the theory of Lord and Shulman, thermoelasticity without energy dissipation of Green and Naghdi, and theories of fractional thermoelasticity proposed earlier. The fundamental solution to the nonhomogeneous space–time-fractional telegraph equation as well as the corresponding thermal stresses are obtained in the axisymmetric case.